By following the instructions here, I was able to fix the problem.
http://striker24x7.blogspot.com/2014/06/vicidial-goautodial-audio-store-white.html
Turns out, the directory that Vicidial was pointing to did not exist. I needed to create the folder and made sure the permissions were okay.
Now, upon clicking the Audio Chooser, this pops up!
P.S. Striker 24x7 - I <3 you!